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力学与实践 ›› 2004, Vol. 26 ›› Issue (3): 0-0.doi: 10.6052/1000-0992-2003-084

• 应用研究 •    

悬臂轴拉杆一阶随机分析的解析解

苏成 范学明   

  1. 广州华南理工大学建筑学院土木工程系 广州华南理工大学土木工程系 510640
  • 收稿日期:2003-03-05 修回日期:2003-07-07 出版日期:2004-06-10 发布日期:2004-06-10

EXACT SOLUTIONS FOR FIRST-ORDER STOCHASTIC ANALYSIS OF AXIALLY-LOADED CANTILEVER BARS

  • Received:2003-03-05 Revised:2003-07-07 Online:2004-06-10 Published:2004-06-10

摘要: 针对悬臂轴拉杆在自由端受集中力问题进行了随机分析,其中考虑了轴拉杆杨氏模量的变 异,在小变异情况下获得了不同相关结构与相关长度下问题的解析解,并就结果对相关结构 的敏感性进行了讨论.

关键词: 随机分析,相关结构,相关长度,解析解, analytical solutions

Abstract: This paper presents a stochastic analysis of an axially-loaded cantilever bar with the Young's modulus being considered as a random field. For a small variation, the stochastic governing differential equation and the boundary conditions of the problem are first decomposed into two sets of equations and conditions corresponding to a mean value problem and a deviation problem, respectively. According to the similarity between the above two sets of equations and conditions, analytical solutions corresponding to different covariance structures and fluctuation scales are then obtained. On this basis, the sensitivity study of the covariance functions on the structural response is carried out. It is shown that different covariance structures have certain effects on the stochastic results, but have little influence on the solutions when the fluctuation scales are either small or large. The exact solutions obtained in this paper may also be used to verify the validity of other numerical methods.

Key words: stochastic analysis, covariance structures, fluctuation scales, analytical solutions